Embedding and wavelet decomposition of spaces of minimal splines

On a sequence of embedded nonuniform grids, chains of embedded spaces of minimal splines (not necessarily polynomial) are constructed. The wavelet decomposition is given. The basis wavelets are compactly supported and admit simple analytic representation. The corresponding decomposition and reconstruction formulas are derived. The variety of spaces under consideration is identified with the variety of complete sequences of points of the direct product of an interval and a projective plane. Bibliography: 20 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 15–31     

Numerical modeling of a XeCl laser excited by microwave discharge

12 , 169 (1987). Reasonably good agreements in the peak output power and laser efficiency have been achieved. Model calculations also predict that an efficiency as high as 2.7% can be obtained once the conditions of the above-mentioned experiments have been optimized. From the consideration that the skin depth effectively limits the absorption length of the microwave pumping and hence the excitable volume, it is concluded that high input power densities (>2 MW/cm³) and higher gas pressures (between 3 and 10 atm) are the preferable conditions to achieve higher efficiency. Preliminary calculations on CCl₄ containing XeCl gas mixtures show that improvement in laser efficiency by several folds may be achieved as a result of the higher intrinsic efficiency of excimer formation. Received: 23 September 1996 / Revised version: 25 March 1997     

The neutron field and radiation shielding efficiency measurement and the luminosity monitoring using the HF RADMON system of the CMS setup

The HF RADMON system monitors radiation environment in the region of the forward calorimeter of the CMS setup. Measurements of neutron fluxes at energies of 7, 8, and 13 GeV are carried out; estimates of the radiation shielding efficiency are obtained. Modernization of the system for operating under high luminosity conditions is completed and its capabilities to be used as an additional luminometer are confirmed.     

Substructure of Intermetallic Thin-Film Cu3Sn

Technical Physics - The crystalline structure of intermetallic Cu3Sn synthesized by successively condensing thin layers of copper and tin on a substrate at 150°C has been studied. Cu3Sn...     

Recrystallization and formation of spheroidal gold particles in amorphous-like AlN–TiB<Subscript>2</Subscript>–TiSi<Subscript>2</Subscript> coatings after annealing and subsequent implantation

The recrystallization of the structure of an X-ray amorphous AlN–TiB₂–TiSi₂ coating containing short-range order regions with characteristic sizes of 0.8–1.0 nm has been performed using a negative gold ion (Au^–) beam and high-temperature annealing. Direct measurements using methods of high-resolution transmission electron microscopy (HRTEM) and energy-dispersive X-ray spectral (EDXS) microanalysis have demonstrated that thermal annealing at a temperature of 1300°C in air results in the formation of nanoscale (10–15 nm) phases AlN, AlB₂, Al₃O₃, and TiO₂, whereas the ion implantation of negative ions Au^– leads to a fragmentation (decrease in the size) of nanograins to 2–5 nm with the formation of spheroidal gold nanocrystallites a few nanometers in size, as well as to the formation of an amorphous oxide film in the depth (near-surface layer) of the coating due to ballistic ion mixing and collision cascades.     

Wavelet decomposition of third height splines of hermitian type

A wavelet decomposition of (nonpolynomial) third height splines of Hermitian type is obtained. Decomposition and reconstruction formulas are constructed in the case of an additional grid point. It is shown that the basis wavelets are three times continuously differentiable and are compactly supported. Bibliography: 12 titles.     

Self-assembled networks of ribbons in molecular hydrogels of cationic deoxycholic acid analogues

Aqueous gels derived from three cationic 24-nor 3,12-dihydroxy cholane (DC) derivatives with N-methyl-2-pyrrolidinone (NMP), N-methylmorpholine (NMM), and 1,4-diazabicyclo[2.2.2]octane (DABCO) at the side chain positions have been exhaustively characterized by small-angle neutron-scattering experiments. Although the molecular structures differ slightly by the heterocycle grafted to the steroid core, the derived gels exhibit a range of structural behaviors at the nanoscale that depart from those observed with simple deoxycholate systems. The NMM-DC aggregates are ribbons with a bimolecular thickness of t = 37 A and an anisotropy of the section b/a approximately 0.1. DABCO-DC exhibits a remarkable transition from ribbons (t = 29.5 A, b/a = 0.18) to thicker cylindrical fibers (R approximately 59 A), involving four original ribbons, upon a concentration increase. The NMP-DC system forms thick cylindrical fibers (R approximately 68 A) with steroid molecules organized in a specific morphology. Bilayered or interdigited structures are formed and favored by the presence of multiple polar interaction centers in the DC molecules. Secondary aggregation mechanisms are invoked in the formation of bundles having a lower cross-sectional anisotropic symmetry and exhibiting Bragg peaks corresponding to molecular length periodicities. The relations between the structural information and the rheological properties are discussed.